Problem: William has a $26$ -liter glass tank. First, he wants to put some marbles in it, all of the same volume. Then, he wants to fill the tank with water until it's completely full. If he uses $85$ marbles, he will have to add $20.9$ liters of water. What is the volume of each marble?
Explanation: Let's say that the volume of a single marble is $V$ liters. Then, the volume of $N$ marbles is $N\cdot V$ liters. In addition, we know that the volume of the tank is $26$ liters. The sum of the water's volume and the marbles' volume should be equal to the tank's volume. We can express this with the equation $W+N\cdot V=26$, where: $W$ represents the volume of water used (in liters) $N$ represents the number of marbles used $V$ represents the volume of a single marble (in liters) We know that if William uses $85$ marbles $(N={85})$, he will have to add $20.9$ liters of water $(W={20.9})$. Let's plug these values into the equation to find the value of $V$. $ \begin{aligned}{20.9}+{85}V&=26\\ 85V&=5.1\\ V&=0.06\end{aligned}$ Therefore, the volume of each marble is $0.06$ liters. To find how much water is necessary if William uses $200$ marbles, we can plug $N=200$ into the equation and solve for $W$. $ \begin{aligned}W+200\cdot 0.06&=26\\ W&=26-12\\ W&=14\end{aligned}$ The volume of each marble is $0.06$ liters. William needs $14$ liters of water if he uses $200$ marbles.